Structural Optimization of Linearly Elastic Structures Using the Homogenization Method

  • N. Kikuchi
  • K. Suzuki
Part of the International Centre for Mechanical Sciences book series (CISM, volume 325)


There are three major structural optimization problems of a linearly elastic structure; namely, 1) sizing, 2) shape, and 3) layout(topology) optimization problems. The characteristics of these problems can be summarized as follows:


Design Variable Design Domain Volume Constraint Homogenization Method Layout Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Banichuk, N.V., Problems and methods of optimal structural design, Plenum Press, New York (1983)CrossRefGoogle Scholar
  2. [2]
    Cheng, K.T., and Olhoff, N., An investigation concerning optimal design of solid elastic plates, In t . J. Solids and Structures 17 (1981) 305–323CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    Lurie, K.A., Fedorov, A.V., and Cherkaev, A.V., Regularization of optimal design problems for bars and plates, Parts I and II, J. Optim. Theory Appl. 37(4) (1982) 4999–521, 523–543CrossRefMathSciNetGoogle Scholar
  4. [4]
    Bendsoe, M.P., Generalized plate models and optimal design, in J.L. Eriksen, D. Kinderlehrer, R. Kohn and J.L. Lions, eds., Homogenization and effect moduli of materials and media, The IMA Volumes in Mathematics and Its Applications, Spriger-Verlag, Berlin, 1986, 1–26CrossRefGoogle Scholar
  5. [5]
    Palmer, A.C., Dynamic Programing and Structural Optimization, in R.H. Gallagher and O.C. Zienkiewicz, eds., Optimum Structural Design, John Wiley & Sons, Chichester (1973) 179–200Google Scholar
  6. [6]
    Murat, F., and Tartar, L., Optimality conditions and homogenization, in A. Marino, L. Modica, S. Spagnolo, and M. Degiovanni, eds., Nonlinear variational problems, Pitman Advanced Publishing Program, Boston, 1985, 1–8Google Scholar
  7. Kohn, R., and Strang, G., Optimal Design and relaxation of variational problems, Parts I, II and III, Communications on Pure and Applied Mathematics,XXXIX (1986) 113–137, 139–182, 353–378Google Scholar
  8. [8]
    Bendsoe, M.P., and Kikuchi, N., Generating optimal topologies in structural design using a homogenization method, Comput. Mechs. Appl. Mech. Engrg., 71 (1988) 197–224CrossRefMathSciNetGoogle Scholar
  9. [9]
    Suzuki, K., and Kikuchi, N., Shape and topology optimization using the homogenization method, Comput. Mechs. Appl. Mech. Engrg. too appear (1941)Google Scholar
  10. [10]
    Bennett, J. A. and Botkin, M.E., Structural shape optimization with geometric problem description and adaptive mesh refinement, AIM J., 23 (3), 458–464 (1985)Google Scholar
  11. [11]
    Fukuda, J., and Suhara, J., Automatic Mesh Generation for Finite Element Analysis, in Advance, in: Computational Methods in Structural Mechanics and Design, (Ed. Oden, J.T., and Yamamoto, Y.), UAH Press, Huntsville, Alabama, U.S. (1972)Google Scholar
  12. [12]
    Cavendish, J.C., Automatic Triangulation of Arbitrary Planar Domains for the Finite Element Method, International Journal for Numerical Methods in Engineering, 8, 679–696 (1974)CrossRefzbMATHGoogle Scholar
  13. [13]
    Lo, S.H., A New Mesh Generation Scheme for Arbitrary Plannar Domains, International Journal for Numerical Methods in Engineering, 21, 1403–1426 (1985)CrossRefzbMATHGoogle Scholar
  14. [14]
    Shephard, M.S., and Yerry, M.A., An approach to automatic finite element mesh generation, in: Computers in Engineering 1982, 3., edited by Hulbert, L.E., The American Society of Mechanical Engineers, New York, 21–28 (1982)Google Scholar
  15. [15]
    Tezuka, A, A Development of Automatic Mesh Generator with Arbitrary Geometry-Based Input Description, MS Thesis, Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI, U.S., (1988)Google Scholar
  16. [16]
    Eschenauer, H., Post, P.U. and Bremicker. M., Einsatz der Optimienongsprozedur SAPOP zur Auslegung von Bauteilkomponenten. Bauingenieur 63, 515–526 (1988)Google Scholar
  17. [17]
    Bremicker,M., Eschenauer, H., Post, P., Optimization Procedure SAPOP - A General Tool for Multicriteria Structural Design. In: Eschenauer, H., Koski, J., Osyczka, A., Multicriteria Design Optimization. Berlin, Springer Verlag (to appear May 1990 )Google Scholar
  18. [18]
    Bremicker, M., Chirehdast, M., Kikuchi, N., and Papalambros, P.Y., Integrated Topology and Shape Optimization in Structural Design, Journal of Mechanics of Structures and Machines, (in Review) 1989Google Scholar

Copyright information

© Springer-Verlag Wien 1992

Authors and Affiliations

  • N. Kikuchi
    • 1
  • K. Suzuki
    • 1
  1. 1.University of MichiganAnn ArborUSA

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